The 1.x versions of Omeka won't do much with jpeg2000, raw, psd, or most of those text document formats, but it will allow you to upload them assuming you allow those types/extensions. Plugins can be used to add display options for filetypes Omeka doesn't handle by default.

For most image formats, Omeka will automatically make thumbnails and display those on pages, while keeping the original file. Omeka will extract EXIF and IPTC metadata from JPEG and TIFF files. I'm not so sure about XMP, but I believe that can be stored within EXIF data, and Omeka can pick it out if that's the case. Video files will show a browser plugin player.

In Omeka 2.0 (not yet released), the thumbnailing is expanded to work on whatever your server supports, so thumbnails of jpeg2000 files, pdf files and other formats become possible, assuming your ImageMagick and server setup have the proper support.